Puzzle to turn into matrix game? Help!

Five players each have a different (given) number of mice in their bags. Each player also has his own hidden mouse treat behind his back, which mice may or may not be able to sense. All players open their bags at the same time, allowing mice to move freely between bags if they so choose. At the same time, each player closes his bag and counts how many mice he now has in his bag. Mice are identifiable by the bag they originally occupied. What can be said for the mice’s preference for each player’s hidden treat? What relationships can be identified between the players and mice movement with this information?

2. Relevant equations

5 x 5 matrix...?

3. The attempt at a solution

Initially I designed a 5x5 matrix, with wins (and losses) between players representing a linear transformation. But I have no idea how to speak intelligently about it, or even grasp the question's theoretical backbone!